The drawing of glass in sheet form from a molten pool is one of the oldest of the industrial arts. The desirability of maintaining the edges of the drawn sheet at a significant temperature differential below the temperature of the central portions of the sheet has long been known in the art and a variety of methods and apparatuses have been heretofore proposed for accomplishing such differential cooling of the drawn sheet. All of such prior art methods and apparatuses have, however, proven to be ineffective when an attempt is made to apply same to the drawing of glass film having a thickness not in excess of 0.003 inches and generally on the order of 0.0005 inches. For example, the prior art suggests cooling of the edges of the drawn sheet of glass by blowing cool air on the edges. Any blast of cooling air applied to a glass film of the thickness described would result in the complete destruction of the film. Other prior art patents have suggested placement of electrodes within the molten glass body at a position immediately adjacent the points at which the edges of the glass sheet are drawn from the molten glass. The drawn film is so narrow, viz. 12 to 24 inches, and the amount of glass withdrawn from a molten body in the fabrication of thin films is so small that no effective differential heating effect supposedly produced by the insertion of electrodes is achieved.